Existence of solution for Kirchhoff model problems with singular nonlinearity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.14232/ejqtde.2021.1.82

Equations M. Montenegro

引用次数: 0

Abstract

We study the fourth order Kirchhoff equation Δ2u−(a+b∫Ω|∇u|2)γΔu=f(u) in Ω with −Δu>0 and u>0 in Ω, and Δu=u=0 on ∂Ω, where f(t)=α1tθ+λtq+μt+g(t) for t≥0, g has subcritical growth, α>0, λ>0, μ≥0, 0<θ<1, 0<q<1, γ≥0, a>0, b≥0. We use the Galerkin projection method to show the existence of solution under some boundedness restriction on α,λ,μ. In some cases we study the behavior of the norm of the solution u as λ→0 and as λ→∞. Similar issues are addressed for the equation (a+b∫Ω|∇u|2)γΔ2u−ϱΔu=f(u), ϱ≥0.

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奇异非线性Kirchhoff模型问题解的存在性

我们学习第四阶基尔霍夫方程Δ2 u−(a + b∫Ω|∇u | 2)γΔu = f (u)在Ω−Δu > 0Ωu > 0,和∂Δu = = 0Ω,f (t) =α1 tθ+λtq +μt t≥0 + g (t), g亚临界增长,α> 0,λ> 0,μ≥0,0θ1,0 q1,γ≥0 > 0,b≥0。利用伽辽金投影法证明了在α，λ，μ的有界约束下解的存在性。在某些情况下，我们研究了解u的范数在λ→0和λ→∞时的行为。解决类似问题的方程(a + b∫Ω|∇u | 2)γΔ2 u−ϱΔu = f (u),ϱ≥0。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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